Oscar-winning "The Hurt Locker" director Kathryn Bigelow looks to be adding some more big guns to the cast of her next film, the highly-anticipated dramatization of the Navy SEAL hunt for Osama Bin Laden.

Although no deals are in place, The Hollywood Reporter says that Jessica Chastain ("Tree of Life"), Mark Strong ("Tinker, Tailor, Solider, Spy") and Edgar Ramirez ("Carlos") are all circling the project. Separately, Chastain confirmed to HitFix in December that she was excited to begin shooting Bigelow's new film in January.

They would join cast members Joel Edgerton ("Warrior"), Chris Pratt ("Parks and Recreation") and Jason Clarke ("Public Enemies"). The as-yet-untitled film will center on Navy SEAL Team 6 as it searches out the Al Qaeda mastermind, who was finally killed in May of 2011 after nearly a decade of hiding.

The film has come under scrutiny several times, due to allegations that the producers were supplied with top secret intelligence from the White House during consultations. In a clear effort to somewhat distance the film from politics, Sony aims to release it after the fall election, on December 19.

Chastain, who had a very busy 2011 with both "The Help" and "Tree of Life" garnering awards buzz (plus "The Debt" and "Take Shelter"), was set to star opposite Tom Cruise in the SF film "Oblivion" but it's unclear if that film would potentially conflict with the Bin Laden project.